An Implementation of the Lê–Teissier Method for Computing Local Euler Obstructions

Abstract

Local Euler obstruction of a hypersurface with possibly positive dimensional singularities, a constructible function on the hypersurface, is considered in the context of symbolic computation. It is shown that the method due to Le and Teissier (Ann Math 114:457–491, 1981) that requires genericity conditions for computing local Euler obstructions can be realized as an algorithm in a deterministic way. The key ideas of the proposed algorithm are the use of comprehensive Grobner systems and of parametric local cohomology systems.